What are the divisors of 3466?

1, 2, 1733, 3466

There is a total of 4 positive divisors.
The sum of these divisors is 5202.
The arithmetic mean is 1300.5.

2 even divisors

2, 3466

2 odd divisors

1, 1733

How to compute the divisors of 3466?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 3466 by each of the numbers from 1 to 3466 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

3466 / 1 = 3466 (the remainder is 0, so 1 is a divisor of 3466)
3466 / 2 = 1733 (the remainder is 0, so 2 is a divisor of 3466)
3466 / 3 = 1155.3333333333 (the remainder is 1, so 3 is not a divisor of 3466)
...
3466 / 3465 = 1.0002886002886 (the remainder is 1, so 3465 is not a divisor of 3466)
3466 / 3466 = 1 (the remainder is 0, so 3466 is a divisor of 3466)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 3466 (i.e. 58.87274411814). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

3466 / 1 = 3466 (the remainder is 0, so 1 and 3466 are divisors of 3466)
3466 / 2 = 1733 (the remainder is 0, so 2 and 1733 are divisors of 3466)
3466 / 3 = 1155.3333333333 (the remainder is 1, so 3 is not a divisor of 3466)
...
3466 / 57 = 60.80701754386 (the remainder is 46, so 57 is not a divisor of 3466)
3466 / 58 = 59.758620689655 (the remainder is 44, so 58 is not a divisor of 3466)